Until Megyn Kelly, no prime-time Fox News anchor had tried to leap from partisan basic cable to the more pedigreed world of network news.

Less than a month into her tenure at NBC, Ms. Kelly and her new employer — which has placed a multimillion-dollar bet on her success — are learning just how daunting the transition can be.

Even before it airs on Sunday, Ms. Kelly’s interview with Alex Jones, the conspiracy-monger and influential voice of the so-called alt-right, a far-right, white nationalist movement, has generated a fierce backlash, just as the anchor is introducing herself to a broader audience.

Parents of children killed in the 2012 Sandy Hook elementary school shooting, which Mr. Jones called a hoax, asked NBC to spike the interview, saying it was extremely hurtful for her to offer a platform for Mr. Jones’s views. Ms. Kelly was disinvited from a Sandy Hook charity event and accused by some viewers of chasing ratings by infecting NBC with Fox News-style conservatism.

On Friday, NBC’s Connecticut affiliate said it would not broadcast Ms. Kelly’s show this Sunday, citing community concerns. In an internal memo obtained by The New York Times, the station, WVIT, said that for many of its viewers and employees, including Sandy Hook parents, “those wounds are understandably still so raw.”

Earlier in the day, Mr. Jones’s website, InfoWars, published audio of Ms. Kelly cajoling and flattering her interview subject as she tried to secure his cooperation for the segment. “I’m not looking to portray you as some boogeyman,” Ms. Kelly can be heard saying. Assurances of fair coverage are standard practice in television journalism, where anchors seeking access routinely present their intentions in the best possible light. NBC is standing by Ms. Kelly, urging viewers to withhold judgment until the segment airs.

But the firestorm has been an unwelcome surprise at the network. NBC is banking on Ms. Kelly, who is drawing a salary reported to be about$15 million, as its next flagship star.

Her new show already faced an uphill fight against CBS’s “60 Minutes,” the No. 1 show in television news. And Ms. Kelly is about three months away from taking over the 9 a.m. hour on the “Today” show, a coveted soft-news time slot.

No TV personality wants to face the wrath of families of victims of a school shooting. And Ms. Kelly, who is predominantly known as a face of a conservative-leaning cable news network, does not have a reservoir of good will with NBC’s bigger audience to fall back on.

“It’s Jimmy Fallon tousling Trump’s hair,” said Martin Kaplan, director of the Norman Lear Center for media and society at the University of Southern California, likening the Kelly-Jones tempest to the moment last fall that is widely considered to have caused lasting damage to Mr. Fallon, NBC’s “Tonight Show” host.

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Ms. Kelly on the set of “Sunday Night With Megyn Kelly.”CreditBrian Doben/NBC News

Journalists, by and large, have offered support for Ms. Kelly, saying that Mr. Jones, who has spoken to President Trump and offered him advice, is certainly a worthy subject for journalistic scrutiny. Mr. Jones’s beliefs, however suspect or offensive, reach a sizable audience around the country thanks to his popular radio show and website.

Other shows, like Piers Morgan’s prime-time CNN show and ABC’s “Nightline,” featured interviews with Mr. Jones in 2013.

“Megyn is a very good journalist, and I expect, especially in light of everything that’s been said this week, that he will be held to account,” Jeff Zucker, the president of CNN and former chief executive of NBC, said during a question-and-answer session with journalists this week. But Mr. Zucker added that NBC executives had “done themselves no favors” in the way the segment has been marketed to viewers.

He also cited a damaging photograph of Ms. Kelly wearing sunglasses and smiling alongside Mr. Jones on the day of their interview. The image was distributed by Mr. Jones, not NBC, but by posing for it, Ms. Kelly conveyed the sense of a cozy encounter rather than a cross-examination.

“If you are going to do this story, the tease needs to be you holding up a picture of the dead kids at Sandy Hook and saying, ‘How dare you?’ And that’s what you need to do,” Mr. Zucker said.

NBC has not released a transcript of Ms. Kelly’s interview, leading some to speculate that her interrogation of Mr. Jones over his more contentious views — for instance, that Sandy Hook was a hoax and the Sept. 11 terrorist attacks were carried out by the United States government — was less than ferocious.

NBC executives were retooling the segment in light of the criticism, and Ms. Kelly has contacted parents of Sandy Hook victims in recent days, asking if they would be willing to speak on-camera to respond to Mr. Jones.

Nicole Hockley and Mark Barden, parents of two of the 20 children who died at the school in Newtown, Conn., spoke with Ms. Kelly this week about an appearance on her show. “We declined to participate,” Ms. Hockley wrote in a text message on Friday.

Another Sandy Hook parent, who requested anonymity because of privacy concerns, said Ms. Kelly had made the case this week that by coming on her show, families could best explain to viewers how Mr. Jones’s actions had hurt them. The parent declined to participate, saying it would create a sense of false equivalence with what they considered Mr. Jones’s outrageous perspective.

NBC said on Friday that at least one Sandy Hook parent was expected to appear in the segment. “We remain committed to giving viewers context and insight into a controversial and polarizing figure, how he relates to the president of the United States and influences others, and to getting this serious story right,” the network said in a statement. “Tune in Sunday.”

The storm shows few signs of abating. Late Thursday, a law firm representing several Sandy Hook families sent a letter to NBC warning that “airing the interview will cause serious emotional distress to dozens of Sandy Hook families.” At least one advertiser, JPMorgan Chase, has pulled its sponsorship of Sunday night’s show, and Ms. Kelly said this week that she was taken aback by the level of backlash at the Jones segment.

Chris Cuomo, the CNN anchor, said he believed network executives would be toiling until the last minute to ensure that Sunday’s segment was seen as being responsive to the public criticism. “Coming from that world, I do not envy the job those producers and editors have right now,” Mr. Cuomo said.

Kristin Hussey and Maya Salam contributed reporting.

A version of this article appears in print on , on Page B3 of the New York edition with the headline: Kelly and NBC Quickly Land on the Hot Seat. Order Reprints | Today’s Paper | Subscribe